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  <div class="section" id="numpy-dot">
<h1>numpy.dot<a class="headerlink" href="#numpy-dot" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.dot">
<code class="sig-prename descclassname">numpy.</code><code class="sig-name descname">dot</code><span class="sig-paren">(</span><em class="sig-param">a</em>, <em class="sig-param">b</em>, <em class="sig-param">out=None</em><span class="sig-paren">)</span><a class="headerlink" href="#numpy.dot" title="Permalink to this definition">¶</a></dt>
<dd><p>Dot product of two arrays. Specifically,</p>
<ul>
<li><p>If both <em class="xref py py-obj">a</em> and <em class="xref py py-obj">b</em> are 1-D arrays, it is inner product of vectors
(without complex conjugation).</p></li>
<li><p>If both <em class="xref py py-obj">a</em> and <em class="xref py py-obj">b</em> are 2-D arrays, it is matrix multiplication,
but using <a class="reference internal" href="numpy.matmul.html#numpy.matmul" title="numpy.matmul"><code class="xref py py-func docutils literal notranslate"><span class="pre">matmul</span></code></a> or <code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">&#64;</span> <span class="pre">b</span></code> is preferred.</p></li>
<li><p>If either <em class="xref py py-obj">a</em> or <em class="xref py py-obj">b</em> is 0-D (scalar), it is equivalent to <a class="reference internal" href="numpy.multiply.html#numpy.multiply" title="numpy.multiply"><code class="xref py py-func docutils literal notranslate"><span class="pre">multiply</span></code></a>
and using <code class="docutils literal notranslate"><span class="pre">numpy.multiply(a,</span> <span class="pre">b)</span></code> or <code class="docutils literal notranslate"><span class="pre">a</span> <span class="pre">*</span> <span class="pre">b</span></code> is preferred.</p></li>
<li><p>If <em class="xref py py-obj">a</em> is an N-D array and <em class="xref py py-obj">b</em> is a 1-D array, it is a sum product over
the last axis of <em class="xref py py-obj">a</em> and <em class="xref py py-obj">b</em>.</p></li>
<li><p>If <em class="xref py py-obj">a</em> is an N-D array and <em class="xref py py-obj">b</em> is an M-D array (where <code class="docutils literal notranslate"><span class="pre">M&gt;=2</span></code>), it is a
sum product over the last axis of <em class="xref py py-obj">a</em> and the second-to-last axis of <em class="xref py py-obj">b</em>:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">dot</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)[</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">,</span><span class="n">k</span><span class="p">,</span><span class="n">m</span><span class="p">]</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">,</span><span class="n">j</span><span class="p">,:]</span> <span class="o">*</span> <span class="n">b</span><span class="p">[</span><span class="n">k</span><span class="p">,:,</span><span class="n">m</span><span class="p">])</span>
</pre></div>
</div>
</li>
</ul>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>a</strong><span class="classifier">array_like</span></dt><dd><p>First argument.</p>
</dd>
<dt><strong>b</strong><span class="classifier">array_like</span></dt><dd><p>Second argument.</p>
</dd>
<dt><strong>out</strong><span class="classifier">ndarray, optional</span></dt><dd><p>Output argument. This must have the exact kind that would be returned
if it was not used. In particular, it must have the right type, must be
C-contiguous, and its dtype must be the dtype that would be returned
for <em class="xref py py-obj">dot(a,b)</em>. This is a performance feature. Therefore, if these
conditions are not met, an exception is raised, instead of attempting
to be flexible.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>output</strong><span class="classifier">ndarray</span></dt><dd><p>Returns the dot product of <em class="xref py py-obj">a</em> and <em class="xref py py-obj">b</em>.  If <em class="xref py py-obj">a</em> and <em class="xref py py-obj">b</em> are both
scalars or both 1-D arrays then a scalar is returned; otherwise
an array is returned.
If <em class="xref py py-obj">out</em> is given, then it is returned.</p>
</dd>
</dl>
</dd>
<dt class="field-odd">Raises</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>ValueError</strong></dt><dd><p>If the last dimension of <em class="xref py py-obj">a</em> is not the same size as
the second-to-last dimension of <em class="xref py py-obj">b</em>.</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="numpy.vdot.html#numpy.vdot" title="numpy.vdot"><code class="xref py py-obj docutils literal notranslate"><span class="pre">vdot</span></code></a></dt><dd><p>Complex-conjugating dot product.</p>
</dd>
<dt><a class="reference internal" href="numpy.tensordot.html#numpy.tensordot" title="numpy.tensordot"><code class="xref py py-obj docutils literal notranslate"><span class="pre">tensordot</span></code></a></dt><dd><p>Sum products over arbitrary axes.</p>
</dd>
<dt><a class="reference internal" href="numpy.einsum.html#numpy.einsum" title="numpy.einsum"><code class="xref py py-obj docutils literal notranslate"><span class="pre">einsum</span></code></a></dt><dd><p>Einstein summation convention.</p>
</dd>
<dt><a class="reference internal" href="numpy.matmul.html#numpy.matmul" title="numpy.matmul"><code class="xref py py-obj docutils literal notranslate"><span class="pre">matmul</span></code></a></dt><dd><p>‘&#64;’ operator as method with out parameter.</p>
</dd>
</dl>
</div>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="go">12</span>
</pre></div>
</div>
<p>Neither argument is complex-conjugated:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">([</span><span class="mi">2</span><span class="n">j</span><span class="p">,</span> <span class="mi">3</span><span class="n">j</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="n">j</span><span class="p">,</span> <span class="mi">3</span><span class="n">j</span><span class="p">])</span>
<span class="go">(-13+0j)</span>
</pre></div>
</div>
<p>For 2-D arrays it is the matrix product:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">]]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
<span class="go">array([[4, 1],</span>
<span class="go">       [2, 2]])</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">3</span><span class="o">*</span><span class="mi">4</span><span class="o">*</span><span class="mi">5</span><span class="o">*</span><span class="mi">6</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">3</span><span class="o">*</span><span class="mi">4</span><span class="o">*</span><span class="mi">5</span><span class="o">*</span><span class="mi">6</span><span class="p">)[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">((</span><span class="mi">5</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">3</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)[</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span>
<span class="go">499128</span>
<span class="gp">&gt;&gt;&gt; </span><span class="nb">sum</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">2</span><span class="p">,:]</span> <span class="o">*</span> <span class="n">b</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,:,</span><span class="mi">2</span><span class="p">])</span>
<span class="go">499128</span>
</pre></div>
</div>
</dd></dl>

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